Are my dimensional analysis question correct

[JakePearson]

are these dimensional analysis questions correct

A = area
V = volume
v = speed
p = density

1. VA / v = L³ L² L^-1 T^-1 = L⁴T^-1

2. V^2/3 A = (LT^-1)^2/3 L² = L^2/3 T^-2/3 x L² = L^10/3T^-2/3

3. 3A³ + 2V² = A³ = L⁶
V² = (L/T)² = L²T^-2 = L⁴T^-2

are these correct

 

[cepheid]

For the first one, you made a mistake on the exponent on T. 1/[velocity] has dimensions of [time]/[length].

For the second one, you made a mistake on the L exponent. (2 + 6 is not equal to 10).

For the third one, the original equation doesn't make sense.

 

[JakePearson]

for;
v^2/3A

i got an answer of = L^4/3T^-2/3

is this correct

 

[cepheid]

No. Do you understand the laws of exponents? When you multiply two powers, you ADD their exponents. For example:

a^xa^y = a^x+y